On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of ψ^α exponential-typeorbitals (ψ^α-ETOs, α= 1,0, -1, -2, …) the seriesexpansion formulas for the noninteger n^* Slater-type orbitals (NISTOs)in terms of integer n Slater-type orbitals (ISTOs) are derived. Theseformulas enable us to express the overlap integrals with NISTOs through theoverlap integrals over ISTOs with the same and different screeningconstants. By calculating concrete cases the convergence of the series forarbitrary values of noninteger principal quantum numbers and screeningconstants of NISTOs and internuclear distances is tested. The accuracy ofthe results is quite high for quantum numbers, screening constants andlocation of STOs.